Finite Group Databasebeta

← Group #270724

Character table — Group #270724

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444448888888888888816161616161616161616161616161616163232
order12222244444422444444444224444444444882444448888888888828
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-11-1111111-1-1-111-1-1-1-1-1-111-1-1-1-111-11
χ4111111111111111111111111-1-1-11-1111111-1-1-1-1-1-111-1-1-1-1-11111-1-11-1
χ5111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-111-1-1-11-1-1-1-1-1-1-111-111-1-1-111111-1-111-1-11-1
χ8111111111111111111-1-1-1-111-1-1-11-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-111-11
χ9111111111111-1-111-1-111111-1111-1111-1-1-1-111-111-1111-1-1-1-1-1-1-1-1-1-111
χ10111111111111-1-111-1-111111-1111-1111-1-1-1-111-1-1-1-1-1-11-1-111111111-1-1
χ11111111111111-1-111-1-111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-11
χ12111111111111-1-111-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1-1111-11111-1-1-1-1111-1
χ13111111111111-1-111-1-1-1-1-1-11-1111-11-1-11111-1-1-111-111-111-1-1-1-11111-1-1
χ14111111111111-1-111-1-1-1-1-1-11-1111-11-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ15111111111111-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-111-1-1111-1
χ16111111111111-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111-1-11111-1-111-1-111-1-1-11
χ17222222222-2-2200-2-2002222-202-2-202-2-2000022000000-2000000000000
χ18222222222-2-2200-2-2002222-20-2220-2-2-20000-2-20000002000000000000
χ19222222222-2-2200-2-200-2-2-2-2-202-2-202220000-2-20000002000000000000
χ20222222222-2-2200-2-200-2-2-2-2-20-2220-222000022000000-2000000000000
χ21222222-2-2-222-2222-2-2-20000-22000-200000000000002-2000002-2000000
χ22222222-2-2-222-2222-2-2-20000-22000-20000000000000-2200000-22000000
χ23222222-2-2-222-2-2-22-2220000-2-2000200000000000002-200000-22000000
χ24222222-2-2-222-2-2-22-2220000-2-200020000000000000-22000002-2000000
χ252222-2-22-2222-222-2-2-2-200002-222-22-200000000200-2000000000000000
χ262222-2-22-2222-222-2-2-2-200002-2-2-222200000000-2002000000000000000
χ272222-2-22-2222-2-2-2-2-22200002222-2-2-200000000-2002000000000000000
χ282222-2-22-2222-2-2-2-2-222000022-2-22-2200000000200-2000000000000000
χ292222-2-22-22-2-2-20022000000-202-220-2002i2i−2i−2i0000000002i−2i0000000000
χ302222-2-22-22-2-2-20022000000-202-220-200−2i−2i2i2i000000000−2i2i0000000000
χ312222-2-22-22-2-2-20022000000-20-22-202002i2i−2i−2i000000000−2i2i0000000000
χ322222-2-22-22-2-2-20022000000-20-22-20200−2i−2i2i2i0000000002i−2i0000000000
χ332222-2-2-22-222222-22220000-2-2000-200000000002-20000002-200000000
χ342222-2-2-22-222222-22220000-2-2000-20000000000-22000000-2200000000
χ352222-2-2-22-2222-2-2-22-2-20000-22000200000000002-2000000-2200000000
χ362222-2-2-22-2222-2-2-22-2-20000-2200020000000000-220000002-200000000
χ37444444-4-4-4-4-4-400-440000004000000000000000000000000000000000
χ384444-4-4-44-4-4-44004-40000004000000000000000000000000000000000
χ3944-4-4000004-4000004i−4i2i2i−2i−2i00000002i−2i2-22-2000000000000000000000
χ4044-4-4000004-4000004i−4i−2i−2i2i2i0000000−2i2i-22-22000000000000000000000
χ4144-4-4000004-400000−4i4i2i2i−2i−2i00000002i−2i-22-22000000000000000000000
χ4244-4-4000004-400000−4i4i−2i−2i2i2i0000000−2i2i2-22-2000000000000000000000
χ4344-4-400000-4404-400002i2i−2i−2i0000000−2i2i2i−2i−2i2i000000000000000000000
χ4444-4-400000-4404-40000−2i−2i2i2i00000002i−2i−2i2i2i−2i000000000000000000000
χ4544-4-400000-440-4400002i2i−2i−2i0000000−2i2i−2i2i2i−2i000000000000000000000
χ4644-4-400000-440-440000−2i−2i2i2i00000002i−2i2i−2i−2i2i000000000000000000000
χ474-4-444-444-400-4000000000000000000000004i−4i0000000000000000000
χ484-4-444-444-400-400000000000000000000000−4i4i0000000000000000000
χ494-4-444-4-4-44004000000000000000000000000000000000000000022−2200
χ504-4-444-4-4-440040000000000000000000000000000000000000000−222200
χ514-4-44-444-4-40040000004-44-40000000000000000000000000000000000
χ524-4-44-444-4-4004000000-44-440000000000000000000000000000000000
χ534-4-44-44-44400-40000000000000000000000000000000000000022−220000
χ544-4-44-44-44400-400000000000000000000000000000000000000−22220000
χ558-88-8000000000000004i−4i−4i4i0000000000000000000000000000000000
χ568-88-800000000000000−4i4i4i−4i0000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).